I'm going to quote the wiki that says "Imitation Magic is activated by touching the Grimoire allowing the user to copy the owner's spells"

Asta is not your typical magic user, so even if pulling out the swords is a spell, the individual unique attributes of the swords or the demon within them isn't tied to the 'summon' spell thus not being able to be imitated through that method.

While Mirror Magic is more self explanatory and an actual 'full' copy of everything involved in Asta's power scheme, his physical self, the attributes, the demon, anything really should be able to be 'mirrored'.